Description: The rank of a power set. Part of Exercise 30 of Enderton p. 207. (Contributed by NM, 22-Nov-2003) (Revised by Mario Carneiro, 17-Nov-2014)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | rankpw.1 | |- A e. _V |
|
| Assertion | rankpw | |- ( rank ` ~P A ) = suc ( rank ` A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rankpw.1 | |- A e. _V |
|
| 2 | unir1 | |- U. ( R1 " On ) = _V |
|
| 3 | 1 2 | eleqtrri | |- A e. U. ( R1 " On ) |
| 4 | rankpwi | |- ( A e. U. ( R1 " On ) -> ( rank ` ~P A ) = suc ( rank ` A ) ) |
|
| 5 | 3 4 | ax-mp | |- ( rank ` ~P A ) = suc ( rank ` A ) |